Work And Energy

Table of Contents (tap to open/close)

  1. Work
    1. Introduction
    2. Work
      1. What is Work?
      2. Not Much ‘Work’ Despite Working Hard
    3. Activity 10.1
      1. Scientific Conception of Work
    4. Activity 10.2
    5. Activity 10.3
    6. Work Done by a Constant Force
      1. How is Work Defined in Science?
        1. Key Points
        2. Examples
    7. Activity 10.4
      1. Example 10.2
  2. Energy
    1. Introduction
    2. Activity 10.5
      1. Understanding Energy
      2. How Energy Works
    3. 10.2.1 Forms of Energy
      1. Think it Over!
      2. Do You Know?
    4. Kinetic Energy
    5. Activity 10.6
    6. Activity 10.7
    7. Understanding Kinetic Energy
      1. Kinetic Energy Calculation
      2. Examples
    8. Potential Energy
      1. Activities to Understand Potential Energy
    9. Activity 10.8
    10. Activity 10.9
    11. Activity 10.10
    12. Activity 10.11
      1. Understanding Potential Energy
    13. Example with a Bow and Arrow (Activity 10.12)
    14. Gravitational Potential Energy
      1. Example 1
      2. Example 2
    15. Energy Forms and Conservation
      1. Are Various Energy Forms Interconvertible?
    16. Activity 10.13
    17. Activity 10.14
    18. Law of Conservation of Energy
      1. Example: Free Fall
    19. Activity 10.15
      1. Think it Over!
  3. Rate of Doing Work
    1. Do We All Work at the Same Rate?
    2. Activity 10.16
    3. Power: How Fast Work is Done
      1. Example 10.7
      2. Example 10.8
    4. Measuring Power Consumption
    5. Activity 10.17
    6. Conclusion
  4. Chapter Summary:

Work

Introduction

  • Living beings need energy for activities: Eating, playing, reading, writing, etc.
  • Animals and machines also need energy: For tasks like pulling carts, carrying loads.

Work

What is Work?

  • Difference in daily life vs. scientific definition:
    • Daily life: Any physical or mental effort.
    • Science: Specific conditions must be met.

Not Much ‘Work’ Despite Working Hard

  • Examples:
    • Kamali studying hard but not doing ‘work’ scientifically.
    • Pushing a rock that doesn’t move.
    • Standing with a load on the head.
    • Climbing stairs or a tree.

Activity 10.1

Questions to consider for daily activities:

  • What is the work being done on?
  • What is happening to the object?
  • Who (what) is doing the work?

Scientific Conception of Work

  • Conditions for work to be done:
    1. A force must act on an object.
    2. The object must be displaced.
  • Examples:
    • Pushing a pebble: Pebble moves.
    • Pulling a trolley: Trolley moves.
    • Lifting a book: Book rises.

Activity 10.2

Daily life situations:

  • List situations involving work.
  • Discuss if work is being done in each.
  • Identify the force and the object involved.

Activity 10.3

  • Situations without work:
    • When an object doesn’t move despite a force.
    • When an object moves without any force acting.
  • List and discuss these situations with friends.

Work Done by a Constant Force

How is Work Defined in Science?

  • When force acts in the direction of displacement:
    • Work done (W) = Force (F) × Displacement (s)
    • 𝑊 = 𝐹 × 𝑠
  • Work done is measured in:
    • Newton metre (N m) or Joule (J)
    • 1 Joule (J) = 1 Newton (N) force × 1 metre (m) displacement
Key Points
  • Work has no direction, only magnitude.
  • If force or displacement is zero:
    • Work done is zero.
Examples
  • Example 10.1:
    • Force = 5 N, Displacement = 2 m
    • Work done = 5 N × 2 m = 10 J
  • Baby pulling a toy car:
    • Force and displacement in the same direction.
    • Work done is positive.
  • Object moving with uniform velocity:
    • Retarding force acts in the opposite direction.
    • Work done is negative.

Activity 10.4

Lift an object up:

  • Work done by you is positive.
  • Gravity does negative work.
  • Positive work: Force in the direction of displacement.
  • Negative work: Force opposite to the direction of displacement.
Example 10.2
  • Porter lifting luggage:
    • Mass of luggage (m) = 15 kg
    • Displacement (s) = 1.5 m
    • Work done (W) = 𝑚𝑔 × 𝑠
    • 𝑊 = 15 kg × 10 m/s2 = 225J
    • Work done is 225 J.

Energy

Introduction

  • Energy is essential for life: The Sun is our main natural energy source.
  • Other energy sources: Nuclei of atoms, Earth’s interior, tides.

Activity 10.5

  • Identify other energy sources.
  • Discuss:
    • How some energy sources are related to the Sun.
    • Which sources are not related to the Sun.

Understanding Energy

  • Daily life examples:
    • Fast cricket ball hitting a wicket.
    • Hammer driving a nail.
    • Winding a toy car.
    • Pressing a balloon until it bursts.
  • Definition: An object with the ability to do work has energy.
    • The object doing the work loses energy.
    • The object on which work is done gains energy.

How Energy Works

  • Process: Energy transfer happens when one object exerts force on another.
    • This causes the second object to move and do work.
  • Measurement:
    • Energy is measured by its capacity to do work.
    • Unit of energy is joule (J).
    • 1 Joule (J) = Energy to do 1 joule of work.
    • Larger unit: kilojoule (kJ) = 1000 J.

10.2.1 Forms of Energy

  • Various forms:
    • Mechanical energy (potential + kinetic)
    • Heat energy
    • Chemical energy
    • Electrical energy
    • Light energy
Think it Over!
  • Discussion: How to identify forms of energy.

Do You Know?

  • James Prescott Joule:
    • British physicist known for his work in electricity and thermodynamics.
    • Formulated a law for the heating effect of electric current.
    • Verified the law of conservation of energy.
    • Discovered the mechanical equivalent of heat.
    • The unit “joule” is named after him.

Kinetic Energy

Activity 10.6

Experiment:

  • Drop a heavy ball on a wet sand bed from different heights: 25 cm, 50 cm, 1 m, and 1.5 m.
  • Observe and compare the depth of depressions.
  • Discuss which depression is deepest and why.

Activity 10.7

Experiment:

  • Set up a trolley and wooden block.
  • Place a known mass on the pan to make the trolley move and hit the block.
  • Measure how far the block moves (displacement).
  • Increase the mass and repeat.
  • Discuss where the energy comes from and compare displacements.

Understanding Kinetic Energy

  • Concept:
    • Moving objects can do work. Faster-moving objects do more work than slower ones.
    • Examples: Bullet piercing a target, wind moving windmill blades.
  • Definition:
    • Kinetic energy is the energy of an object due to its motion.
    • The faster the object moves, the more kinetic energy it has.

Kinetic Energy Calculation

  • Formula:
    • Kinetic Energy
    • 𝑚 = mass of the object
    • 𝑣 = velocity of the object

Examples

  • Example 1:
    • Problem: An object of mass 15 kg is moving with a velocity of 4 m/s.
    • Solution: KE = 1/2 × 15 kg × (4 m/s)2 = 120 J.
  • Example 2:
    • Problem: Calculate the work needed to increase the velocity of a car (1500 kg) from 30 km/h to 60 km/h.
    • Solution:
      • Convert velocities: 30 km/h = 25/3 m/s , 60 km/h = 50/3 m/s.
      • Initial KE = 1/2 × 1500 kg × (25/3 m/s)2​ = 156250/3J.
      • Final KE = 1/2 × 1500 kg × (50/3 m/s)2 = 625000/3J.
      • Work done = Final KE – Initial KE = 156250 J.

Potential Energy

Activities to Understand Potential Energy

Activity 10.8

Stretch a Rubber Band:

  • Stretch it and release.
  • Notice it returns to its original shape.
  • The band gains energy when stretched.

Activity 10.9

Stretch a Slinky:

  • Hold one end, move away, and release.
  • Notice how it returns.
  • Energy is gained when stretched or compressed.

Activity 10.10

Wind a Toy Car:

  • Wind it with a key and place on the ground.
  • It moves, showing it gained energy from winding.

Activity 10.11

Lift an Object:

  • Lift an object to a certain height.
  • It can now do work when it falls.
  • Higher it is lifted, more energy it gains.

Understanding Potential Energy

  • Stored Energy:
    • When you stretch a rubber band or wind a toy car, energy is stored as potential energy.
    • Potential energy is the energy an object has due to its position or configuration.

Example with a Bow and Arrow (Activity 10.12)

Make a Bow and Arrow:

  • Stretch the bow’s string, place an arrow, and release.
  • The bow’s shape changes, storing energy, which is then transferred to the arrow as kinetic energy.

Gravitational Potential Energy

  • Lifting Objects:
    • When you lift an object, you do work against gravity.
    • The energy used to lift it is stored as gravitational potential energy.
    • Formula: Potential Energy(𝐸𝑝) = mgh
      • 𝑚 = mass
      • 𝑔 = acceleration due to gravity
      • ℎ= height

Example 1

  • Problem: Find the energy of a 10 kg object at 6 m height.
  • Solution: 𝐸𝑝 = 10 kg × 9.8 m/s2 × 6 m = 588 J

Example 2

  • Problem: Find the height of a 12 kg object with 480 J potential energy.
  • Solution:
    • Given: 𝐸𝑝 = 480 J, g=10m/s2
    • 480 J = 12 kg × 10 m/s2× ℎ

The object is at a height of 4 meters.

Energy Forms and Conservation

Are Various Energy Forms Interconvertible?

Activity 10.13

Discuss Energy Conversion in Nature:

  • How do green plants produce food? They use sunlight.
  • Where do they get their energy from? The Sun.
  • Why does air move? Due to temperature differences.
  • How are fuels like coal and petroleum formed? From ancient organic matter under pressure.
  • What energy conversions sustain the water cycle? Solar energy to water vapor, then gravity causes rain.

Activity 10.14

Human Activities and Gadgets:

  • List activities and gadgets that involve energy conversion.
  • Identify the types of energy conversion in each.

Law of Conservation of Energy

  • Energy Transformation:
    • Energy can be changed from one form to another.
    • Total energy remains the same before and after transformation.
    • Energy can neither be created nor destroyed.
Example: Free Fall
  • Energy Changes in Free Fall:
    • An object of mass 𝑚m falling from height ℎ.
    • Initial potential energy mgh, kinetic energy is zero.
    • As it falls, potential energy converts to kinetic energy.
    • At ground level: ℎ=0, potential energy is zero, kinetic energy is highest.
    • Total energy (potential + kinetic) remains constant: 𝑚𝑔ℎ + 1/2𝑚𝑣2 = constant.

Activity 10.15

Dropping an Object:

  • Drop a 20 kg object from a height of 4 m.
  • Calculate potential and kinetic energy at various points.
  • Use 𝑔 = 10 m/s2 for calculations.
Think it Over!
  • Energy Transformation and Life:
    • What if energy couldn’t transform?
    • Life might not be possible without energy transformation. Do you agree?

Rate of Doing Work

Do We All Work at the Same Rate?

Activity 10.16

Two Children Climbing a Rope:

  • Children A and B weigh the same and climb 8 meters.
  • A takes 15 seconds, B takes 20 seconds.
  • Work done is the same, but A does it faster.
  • Who does more work in 1 second? A, because A is faster.

Power: How Fast Work is Done

  • Definition:
    • Power is the rate of doing work or transferring energy.
    • Formula: Power 𝑃 = 𝑊/𝑡 (Work done 𝑊 divided by time 𝑡).
    • Unit of power is watt (W).
    • 1 watt = 1 joule/second (1 W = 1 J/s).
  • Larger Units:
    • Kilowatt (kW) = 1000 watts (1000 W).

Example 10.7

  • Two Girls Climbing a Rope:
    • Each girl weighs 400 N and climbs 8 meters.
    • Girl A takes 20 seconds:
    • Girl B takes 50 seconds:
    • Girl A is more powerful because she climbs faster.

Example 10.8

  • Boy Running Up Stairs:
    • Boy weighs 50 kg and runs up 45 steps in 9 seconds.
    • Each step is 15 cm high.
    • Height ℎ = 45×0.15 = 6.75 m.
    • Weight 𝑚𝑔=500 N.

Measuring Power Consumption

Activity 10.17

Observing the Electric Meter:

  • Check the electric meter in your house.
  • Note readings at 6:30 am and 6:30 pm for a week.
  • Calculate units consumed during the day and night.
  • Compare with the monthly electricity bill.
  • Estimate electricity consumption of appliances based on their wattage and usage time.

Conclusion

  • Power is a measure of how quickly work is done.
  • Faster work means more power.
  • Understanding power helps us use energy efficiently.

Chapter Summary:

  • Work done on an object = magnitude of force × distance moved in the direction of the force.
  • Unit of work: joule (1 joule = 1 newton × 1 metre).
  • Work done = zero if displacement of the object = zero.
  • An object with the capability to do work has energy.
  • Energy unit = work unit (joule).
  • Object in motion has kinetic energy.
  • Kinetic energy of an object = ½ mv² (m = mass, v = velocity).
  • Energy due to position or shape change is potential energy.
  • Gravitational potential energy = mgh (m = mass, h = height, g = gravity).
  • Law of conservation of energy: Energy can transform from one form to another but can’t be created or destroyed.
  • Total energy remains constant before and after transformation.
  • Energy forms: kinetic, potential, heat, chemical, etc.
  • Sum of kinetic and potential energy = mechanical energy.
  • Power = rate of doing work.
  • SI unit of power: watt (1 W = 1 J/s).
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